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Modeling and optimization of buffers and servers in finite queueing networks

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Abstract

The joint buffer and server optimization problem (BCAP) is a non-linear optimization problem with integer decision variables that optimizes the numbers of buffers and servers such that the resulting throughput is greater than a pre-defined threshold throughput. This work presents a detailed review of the current literature that addresses allocation problems, particularly the BCAP, and a quite effective methodology for solving this problem, which consists of a combination of approximate methods and the Powell algorithm, a derivative-free optimization algorithm. The methodology was applied to networks of queues in the basic topologies series, split, and merge, producing very encouraging results that pointed at robust and homogeneous solutions.

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Acknowledgements

This research has been partially funded by the Brazilian agencies CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico of the Ministry for Science and Technology), under grants 300825/2016-1 and 305515/2018-7, and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais), under grants CEX-PPM-00564-17 and PPM-00321-18.

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Authors and Affiliations

  1. Pró-Reitoria de Pesquisa e Pós-Graduação, Universidade Federal de Ouro Preto, Ouro Preto, MG, 35400-000, Brazil

    H. S. R. Martins

  2. Departamento de Estatística, Universidade Federal de Minas Gerais, Belo Horizonte, MG, 31270-901, Brazil

    F. R. B. Cruz

  3. Departamento de Estatística, Universidade Federal de Ouro Preto, Ouro Preto, MG, 35400-000, Brazil

    A. R. Duarte & F. L. P. Oliveira

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  1. H. S. R. Martins
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  2. F. R. B. Cruz
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  3. A. R. Duarte
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  4. F. L. P. Oliveira
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Correspondence to F. R. B. Cruz.

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Martins, H.S.R., Cruz, F.R.B., Duarte, A.R. et al. Modeling and optimization of buffers and servers in finite queueing networks. OPSEARCH 56, 123–150 (2019). https://doi.org/10.1007/s12597-019-00362-7

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